Combustion Fundamentals

1 2 CombustionFundamentalsTounderstandthefon nationofpollutantsincombustionsystems,we mustfirstunder-standthenatureofthefuelsb eingburned,thethennodynamicsofthecombust ionpro-cess, ,detonations, spectrumoffuelscurrentlyinwidespreaduse, thesimplestincompositionisnaturalgas,whi chconsistsprimarilyofmethanebutincludesa ,buttheyare,atleast, , ,whichconsistsofmeasurementsoftheelement alcompositionofthefuel,generallypresente dasmassfractionsofcarbon,hydrogen,sulfur ,oxygen,nitrogen,andash, "CH4C2H6C3 HshydrocarbonsCOH2H2SN2CO2(106Jm-3) "p,101kPa;T,25 "Sweetened,"H2S (106 Jkg-I)Kerosene( ) < < ,a measureoftheheatreleaseduringcompletecom bustion, ,physicalpropertiesthatinfluencethehandl inganduseofa ,thespecificgravityorAPIgravity,*viscosi ty(possiblyat severaltemperatures),flashpoint(ameasure ofthetemperatureatwhichthefuelissufficie ntlyvolatiletoignitereadily),anddistilla tionprofiles(fractionvaporizedasa functionoftemperature) ,coalsareclassifiedbyrank,a haveundergonerelativelylittlechange, , ,whichidentifiesthedegreeofcoalifactiono fa solidfuel( ).

2 Coalsamplesthathavebeenairdriedaresubjec tedtoa numberofstandardizedteststodeterminethea mountofmoistureinherenttothecoalstructur e,thequantityofvolatilematterreleasedbyt hecoaluponheatingto1200 Kforseveralminutes,andthemassofashornonc ombustibleinorganic(mineral)impuritiesth atremainsafterlowtemper-ature(700to1050K ) ,volatilematter, , *DegreesAPI=[ (specificgravity16 Cjwaterat16 C) ]. (state)CarbonmatterMoistureAshCHN0S(106 Jkg-I)Meta-anthracite(RI) (PA) (PA) (PA) (PA) (CO) (KY) (IL) (CO) (ND) (Australia) (Douglasfir,asreceived) (C02)fromallofthecarbonandwater(H20)from thehydrogen,thatis,fora hydrocarbonfuelwiththegeneralcomposition CnHm,Evenintheidealizedcaseofcompletecom bustion, , ,manyfuelscontainelementsotherthancarbon , ,combustionis notalwayscomplete, composedofoxygen,nitrogen,andsmallamount sofcarbondioxide,argon, ,forourpurposesit is perfectlyreasonabletoconsiderairasa (molebasis) (molebasis)N2 Thusforeverymoleofoxygenrequiredforcombu stion, ,it doeshavea majorimpactonthethermodynamics,chemicalk inetics, "inert" hydrocarbonfuel,CnHm,becomesThusforevery moleoffuelburned, (n+m14)molofairarerequiredand4.

3 78(n+m14)+ [ (n+m14)].Gascompositionsaregenerallyrepo rtedintermsofmolefractionssincethemolefr actiondoesnotvarywithtemperatureorpressu reasdoestheconcentration(moles/unitvolum e).Theproductmolefractionsforcompletecom bustionofthishydrocarbonfuelarenYeo2= (n+m14)+ml4ml2YN2= (n+m14)+ml4YH20= (n+m14)+ml43. 78(n+m14) (CSH1S) + (Oz+ )----+-8 COz+9 HzO+ , ,therefore,114=114= (32+ )1723 Thetotalnumberofmolesofcombustionproduct sgeneratedis8+9+ ,theproductgascompositionis,ona molefractionbasis,8 Yeo,=--= ,O=--5= , (802),(Eventhoughtherearecaseswheresulfu rcompoundsinvolvinghigheroxidationstates ofsulfurorreducedsulfurcompoundsareprodu ced,it isa reasonablefirstapproxima-tiontoassumetha tallofthefuelsulfurforms802,)Uponcombust ion,organicallyboundfuel-nitrogenis convertedtobothNzandNO, ,thenoncombustibleinorganic(mineral)impu ritiesinthefuel,undergoesa numberoftransformationsatcombustiontempe ratures,whichwillalsobeneglectedfortheti mebeing, ,theonlychemicalinformationavailableisit selementalcompositionona massbasis, is , , , , , "asreceived"basis, ,thecompositionisthennormalizedwithrespe cttocarbon:wtElement%mol/ ; ; ;-14= ; ;-32= ; ;-16=.

4 ,thus, ,or,aswrittenhere,themasspermoleofcarbon ,includingash,is100ggM=---= ,ash, , +a(Oz+ )--+COz+ + +( + ) +-4-+ (32+ )g/molCThetotalnumberofmolesofgaseouscom bustionproductspermoleofCisNT=1+ + + ,therefore,IYeo,= ,O= ,= ,= (ppm)ona mole(orvolume)basis,a commonformforpresentingdataonminorspecie sinthegas( ).Fewcombustionsystems areoperatedpreciselyatthestoichiometricc onditionbecauseofthedifficultyofachievin gsuchintimatemixingbetweenfuelandairthat perfectconversionis ,combustorsareoperatedwitha ,theyarenota ,cP,isdefinedasthefuel/airrationormalize d withrespecttothestoichiometricfuel/airra tio,mf/macP=( )(mf/ma)sAlternatively,thestoichiometric ratio,A,istheair/fuelrationormalizedwith respecttostoichiometric,thatis,1cP( )Otherratiosthatappearintheliteratureinc ludethepercentexcessair[EA=(A-1)X100%]an dthepercenttheoreticalair(TA=AX100%). (mflma),(malmf)'H, (coke) , ,4>, (excessair,4> <l) ,toa goodapproximation, ,forexample,thecombustionofmethaneat4>= ,(2) +2H20+ 2 O2+ +2H20+ + :1Ye02=-2-= ,thecombustionconditionisnotstatedinterm sofa fuel/airratiobut,rather,intermsoftheamou ntofoxygeninthecombustionproducts( , ).

5 Theproblemofspecifyingtheproductsofcombu stionismorecomplicatedforfuel-richcombus tion,4>>1, ,somecarbonmonoxide,hydrogen,andpossibly , (CO,CO2,H2,H20,N2), veryshorttimewhena fuelisburned, closedsystemoffixedmassandidentityisequa ltotheheattransfertothesystemfromitssurr oundingsminustheworkdonebythesystemonits surroundings;thatis,foraninfinitesimalch angeofstate,dE=oQ-oW( )Thetotalenergyofthesystem,E,includesthe internalenergy,U,thekineticenergy, ,theheattransfer,oQ,andtheworktransfer,o W, totaldifferential, , ,thekineticandpotentialenergytermscanben e-glected,sowemayexpressthesystemenergyi ntermsoftheinternalenergy,thatis,dU=oQ-o W( )Integratingovera finitechangeofstatefromstateI tostate2,thefirstlawfora closedsystembecomes( )Onlyrarelyintheconsiderationofcombustio nprocessescanwelimitourselvestoa fixedmassina ,thefuelandairenterthecombustionzoneacro sscertainboundaries, ,therefore,toderiveanexpressionforthecha ngeinstateofa fixedvolumeinspace,calledacontrolvolume, ratherthana controlvolumethatispre-scribedbya surface, smallincrementofmass,om, ,wefirstdefinea closedsystemthatincludesboththemateriali nitiallyinthecontrolvolume,massm,energyE },andtheincrementofmasstobeadded, ,themassinthecontrolvolumeism+om,andthee nergyinthecontrolvolumeisE2 Thefirstlawforthechangeofstateofthecombi nedclosedsystemmaybewrittenasE2-(E1+eom) =Q12+pvom-Wxl2whereedenotestheenergy/uni tmass(calledthemassspecificenergy)ofom,v =1/pisthemassspecificvolume,pvomisthewor kdoneonthecombinedsystembytheenvironment asthesmallvolumeismovedacrossthecontrolv olumesurface, ,wefindE2-E1=eom+pvom+Q12-Wxl2 Fora smallincrementofchangeofstate,thisbecome sdE=(e+pv)om+oQ-oWx( ) numberofmassincrementsis straightforward.

6 Simplysumoverallmassflowsenteringandleav ingfromthecontrolvolume, controlvolumewitha numberofenteringandexitingmassflowsmayth enbewrittendE"-"-- +.,u(ej+pvj)fj-~(ei+pvi)fi=Q-WxdtJ,outI, m( )wherehand];arethemassflowrates(masspert ime)leavingorenteringthecontrolvolume,Qi s therateofheattransfertothesystem(energyp ertime),andWxis therateatwhichworkis ,inthecombustionapplica-tionsofinteresth erewecangenerallyneglectthekineticandpot entialenergycontri-butionstothetotalener gy,givingdU"--,,---=,ufihi-,Ufjhj+Q-Wxdt i,inj,outwherethemassspecificenthalpy,Ii ,isdefinedash=Ii+pvTheenergyequationmaya lsobewrittenona molarbasis,thatis,du=~fihi-~fjhj+Q-Wxdti ,inj,out( )( )( )whereh=u+pvdenotesthemolarspecificentha lpy,andfiis +bB----cC+ ( )tothissystemgivescfhc(T1)+dfhD(T1)-afhA (T1)-bfhB(T1)=Qwherenoworkisdonebythecom bustiongasesexceptthatduetoflowsacrossth eboundary,soWx=O.(Theexpansionworkisalre adyaccountedforintheenthalpy.)Themolarfl owofAintothecontrolvolumeisaf,thatofCisc f,andsoon,andthetemperatureisT1 DividingthroughbyfyieldsTheheattransferp ermolethatis requiredtomaintaintheprocessata constanttemper-ature,T=TI>is calledtheenthalpyofreaction,andis giventhesymboll>.

7 Hr(T1), ~T1CI----~ , ( ) speciesrequiresa ,thereferencetemperatureandpressureareta kentobeTo=298 KandPo=1 atm=101kPa, ,however, usuallybasedonthepureelementsintheirpred ominantformsatToandPo,thatis, Cassolidgraphite HasHzgas NasNzgas asOzgas compoundrelativetothereferencestatesofit sconstituentelementsistheenthalpyofthere actionoftheseelementalspeciesthatform1 thesametemperature,T, ,theenthalpiesofformationoftheelementalr eferencecompoundsarezero,72thatis, ;'c,= ;'H2= ;'N2= ;'02=0 Theenthalpyofa compoundatanytemperaturemaybewrittenasth esumoftheenthalpyofformationatthereferen cetemperatureanda ( )( )Thesensibleenthalpytermmaybeevaluatedas anintegralovertemperatureofthespecifiche atatconstantpressure,cp=(ah/aT)p,thatis, h;(T)-h;(To)=[Tcp,;(T')dT' ,asiscommonlythecaseincombustionapplicat ions,onemustaccountforthedependenceofcp, ; ,it issufficienttoapproxi-matethespecifichea tasa linearfunctionoftemperature,( )Thisapproximateformallowscalculationoft hesensibleenthalpyovertherangeoftemperat urescommonlyencounteredincombustioncalcu lations( ,300to3000K)withinabout10%.]

8 ,enthalpiesofformation, ,tabulationsofthermodynamicdatasuchasthe JANAFT hermochemicalTables(StullandProphet,1971 )shouldbeused,ingeneral, chemically reactingopensystemmaynowbewrittenasddU+. ~jj[hj(T)-hj(To)+ ;j(To)]-;L:/;[h;(T)t}.outI,m-hi(To)+ ;;(To)]=Q -Wx( )Ifthechemicalcompositionandthermodynami cpropertiesofthefuelareknown,( )allowsustocalculatetemperaturechanges,h eattransfer, ,considera steady-flowfumacebuminga +bT(Jmol-JK-I)tlhJ(298K)sO(298K)SpeciesN ame(Jmol-I)(Jmol-IK-I)abCCarbon,monatomi c716, (s)Graphite(ref.) , , , , , , sulfide-138, , , , , , , ,monatomic218, , cyanide135, , , ,cis--76, ,trans--78, , , (ref.) , , , , , ,monatomic473, , , , , , , (ref.) , , , Oxygen,monatomic249, , (ref.) (Continued) (g)S(l)S(s)S02S03 NameOzoneSulfur,gasSulfur,liquidSulfur,s olid(ref.)SulfurdioxideSulfurtrioxideCp= a+bT(Jmol~1K~I)t,h;(298K)sO(298K)(Jmol-I )(Jmol-IK-I)ab142, , , , , {[h(T2)-h(To)+Lih;(To)]+2[h(T2)-h(To)+Li h;(To)]HOC022+ [h(T2)-h(To)+Lih;(To)]-[h(Tl)-h(To)+Lih; (To)]CHN24- 2[h(Tl)-h(To)+LihfO(To)] [h(T])-h(To)+Lih.

9 (To)]}02N2whereT]andT2arethetemperatures ofthereactantsenteringandtheproductsleav ingthefurnace, , fuelisnotknown,insteadofusingfunda-menta lthermochemicaldataontheconstituents, calorimeter, ]andPl'Thefuelisburnedcompletely,andthep roductsarecooledtoTl ,( ),atsteady-stateconditionsintheabsenceof anyworkperformedyieldsWehaveusedthefirst lawon amassratherthana molarbasistobeconsistentwiththewayenthal piesofcombustionarecommonlymeasuredandre ported,sinceifthemolec-ularstructureofth efuelisnotknown,wecannotuniquelydefineth eenthalpyofreactionona ,however,readilydetermined,soenthalpyofc ombustiondataarecommonlyreportedon ~-====~~ unitmassoffuelQc=--ffuel=fp~Oducts-ho(T) -ho(T)fair-ho(T)fiproductsI-fuelI-fi=--a irIfuelfuel( )Sincethecombustionprocessisexothennic(r eleasesheat),f1hc( ,itisconvenienttoconvertthemassspecifice nthalpyofcombustiontoa molespecificvalueusingthefonnulaweight, thatis,( )Flowcalorimetermeasurementsoftheheating valueareusuallyperfonnedat tem-peraturesintherange288to298K,introdu cinga ;thatis,allcarbonandhydrogenmustbeoxidiz edtofonnCO2andH20, ,theproductgasesmaycontainseveralpercent H20, , secondcontrolvolumeinthethennodynamicmod el, ( )measuredbyreactor1,1 (TI)=QI{ft, [hw2(TI)-hwl(TI)]=h1 (TI)where1 (TI)isthelatentheatofvaporizationofwater attemperatureTI At298K,1 (298K)=2442Jg-I,or1 (298K)=44,000 Jmol-I.)

10 *Theenthalpyofcom-bustionmeasuredwithH20 presentasliquid(reactors1 and2 combined)is,therefore,--fw-1 (l+2)(TI)=1 (TI)+~1 (T,)it_ Thetermheatingvalueisusedtodenoteheatrel easeduetocombustion,-1 (TI). ,HHV,correspondstotheheatofreactionwhent helatentheatofcondensationofwaterisrecov ered:HHV=-1 (1+2)(T,)Thelowerheatingvalue,LHV,corres pondstothecasewhenthewaterispresentasvap or:LHV=-1 (TI) , flame,waterispresentonlyasvapor. Thusthelowerheatingvalueis ,respectively,thatis,1 (TI)=-LHV1 (TI)=-HHV*TheunitsJmo!-lwill,throughoutt hisbook,meanJg_mo! fuel, ,wemaywritewhere,if themolecularfonnofthefuelisnotknown, ,wefindtheenthalpyoffonnationofthefuel( )Withthisinfonnation, ; ; ; ; ,anditsformulaweightisMf=12+( )(1)= ; + + , generatedforeachmoleoffuel(carbon) heatofvaporizationofwaterat298 KisLlhv(298K)=44, ,200+ ,000-I-567,600J(molC) ,CHu(Td=flhj,C02(T1)+ ,H20(T1) ,o,(T1)-flhcdT1)=-394,088+0,90X(-242,174 ) (0)-(-567,600)-I=-44,440J(molC) ,ontheorderof1 steady-flowcom-bustor, ,burninga ()m(1) + Oz+3,78Nz-COz+'2 HzO+as -1Oz+-4>-Nz( )whereas=I+ [h(T)-h(To)+.]